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a psychology professor assigns letter grades on a test according to the following scheme. a: top 8 % of scores b: scores below the top 8 % and above the bottom 59 % c: scores below the top 41 % and above the bottom 21 % d: scores below the top 79 % and above the bottom 6 % f: bottom 6 % of scores scores on the test are normally distributed with a mean of 70 and a standard deviation of 7.3. find the numerical limits for a d grade. round your answers to the

Respuesta :

The numerical limits for a D grade: 59 to 64

In this question we have been given that the scores on the test are normally distributed with a mean of 70 and a standard deviation of 7.3

μ = 70, σ = 7.3

We need to find the numerical limits for a D grade

D: Scores below the top 79% and above the bottom 6%

So between the 6th and the 21st percentile.

6th percentile:

X when Z has a pvalue of 0.06. So X when Z = -1.555

Z = X - μ/σ

-1.555 = (X - 70)/7.3

X - 70 = -11.35

X = 58.65

X ≈ 59

21st percentile:

X when Z has a pvalue of 0.21. So X when Z = -0.81

Z = X - μ/σ

-0.81 = (X - 70)/7.3

X - 70 = -5.91

X = 64.09

X ≈ 64

Therefore, you get a D if you have a grade between 59 and 64

Learn more about the normal distribution here:

https://brainly.com/question/29509087

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